Level structure of ${}^{31}\mathrm{S}$: From low excitation energies to the region of interest for hydrogen burning in novae through the ${}^{30}\mathrm{P}$($p$,$\gamma$)${}^{31}\mathrm{S}$ reaction

Comprehensive measurements of the excitation energy and spin-parity assignments for states in ${}^{31}\mathrm{S}$ are presented, from the first excited state, up to energies relevant for the ${}^{30}\mathrm{P}$($p$,$\gamma$)${}^{31}\mathrm{S}$ reaction in ONe novae. This reaction rate strongly influences heavy element abundances in novae ejecta. States in ${}^{31}\mathrm{S}$ are paired with their ${}^{31}\mathrm{P}$ analogues using $\gamma$ rays detected with the Gammasphere detector array following the ${}^{28}\mathrm{Si}$(${}^4\mathrm{He}$, $n$) fusion-evaporation reaction. The evolution of mirror energy differences is explored and the results are compared with new shell-model calculations. The excellent agreement observed in this work between experimental data and shell-model calculations provides confidence in using computed estimates in situations where experimental data are unavailable.

Figure 1

Typical $\gamma$-ray angular distributions obtained in the present work. (a) An example of a $\Delta J$ = 0 transition between two $7/2^{+}$ states. (b) Example of a $\Delta J=1$ transition between $7/2^{-}$ and $5/2^{+}$ states. (c) Example of a $\Delta J$ = 2 transition between $7/2^{+}$ and 3/2${}^{+}$ states. Corrections for the detection efficiency of various rings of Gammasphere were taken into account.

Figure 2

$\gamma$-ray spectrum gated on the 1249-keV transition in ${}^{31}\mathrm{S}$. Energies of transitions observed in ${}^{31}\mathrm{S}$ are labeled in keV. The tentative 3910-keV transition is placed in parenthesis. The 3951-keV transition is from a higher-lying ${}^{31}\mathrm{S}$ level reported in the high-spin study performed by Jenkins et al. [6, 7].

Figure 3

$\gamma$-ray spectrum gated on both the 1249- and 2102-keV transitions in ${}^{31}\mathrm{S}$. Energies of observed transitions are given in keV. The 2086-keV transition is from a higher-lying ${}^{31}\mathrm{S}$ level reported in the high-spin study performed by Jenkins et al. [6, 7].

Figure 4

$\gamma$-ray spectrum gated on both the 1165- and 2036-keV transitions in ${}^{31}\mathrm{S}$. Energies of observed transitions are given in keV. The 2086- and 2383-keV transitions are from higher-lying ${}^{31}\mathrm{S}$ levels reported in the high-spin study performed by Jenkins et al. [6, 7].

Figure 5

Comparison of the decay branches observed in the present work for the $A$ = 31 mirror pair (a) ${}^{31}\mathrm{P}$ and (b) ${}^{31}\mathrm{S}$ for states with low excitation energy. The $\gamma$-ray energies are given in keV, while the widths of the arrows represent the observed intensity of the transitions.

Figure 6

Full $\gamma$ decay scheme for the nucleus ${}^{31}\mathrm{S}$ observed in this work. The $\gamma$-ray energies are given in keV, while the widths of the arrows represent the measured intensity of the transitions.

Figure 7

Even-parity excited states in ${}^{31}\mathrm{S}$ (left) plotted together with a comparison to shell-model calculations (right). For the 6138-keV level with a spin-parity (3/2,7/2)${}^{+}$ a 3/2${}^{+}$ assignment is chosen for the purposes of comparison. The 3/2${}_7^{+}$, 3/2${}_8^{+}$, and 7/2${}_5^{+}$ states predicted by the shell model are also shown in the figure but, at present, are not paired with experimentally observed ${}^{31}\mathrm{S}$ levels.

Figure 8

Favored mirror assignments of excited states in ${}^{31}\mathrm{S}$ (left) for excitation energies between 3 and 6.7 MeV. ${}^{31}\mathrm{P}$ excitation energies and spin-parity assignments are from the 2013 Nuclear Data Evaluation [11].

Figure 9

(a) Mirror energy differences observed between odd-parity states in the $T=1/2$ mirror pair ${}^{31}\mathrm{S}$ and ${}^{31}\mathrm{P}$ in the energy region 0–6.7 MeV. (b) Mirror energy differences observed between even-parity states in the $T=1/2$ mirror pair ${}^{31}\mathrm{S}$ and ${}^{31}\mathrm{P}$ in the energy region 0–6.7 MeV.

Figure 10

Plot of difference between experimentally determined ${}^{31}\mathrm{S}$ excitation energies and energies predicted by shell-model calculations.